SOLUTION: A cube measuring 6cm a side is painted red, and then cut up into 216 smaller cubes each {{{1cm^3}}} in volume. How many of the smaller cubes are painted on exactly one surface? How

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Question 1200035: A cube measuring 6cm a side is painted red, and then cut up into 216 smaller cubes each 1cm%5E3 in volume. How many of the smaller cubes are painted on exactly one surface? How many of the smaller cubes have no paint on them at all?
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

        First question was just answered once today.   I repeat my answer here one more time

                        (hoping that you will not post it again . . . )


The large cube consists of   6 x 6 x 6 = 216   small cubes,  in total.

The painted on exactly one surface are those and only those small cubes,
that are at the surface and not contacting with the edges.

The number of such cubes is   6*(4*4) = 6*16 = 96.         ANSWER

The factor/(multiplier)  6  does represent  6  faces of the large cube.

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                        For the second question:


Unpainted are the small cubes that are not at the surface .

The number of such cubes is (6-2)*(6-2)*(6-2) = 4*4*4 = 64.         ANSWER


Solved.